I\'m currently in the process of trying to get Gitlab omnibus installed on my private Debian server, and it works perfectly on port 80, the problem is I also have an Apache
Most likely you have another service listening on 8080, I think the omnibus install have some service hooking 8080 - just use 8081 instead.
Edit: I just did a quick search and found that it's the unicorn server that is listening to 8080 with the original omnibus installer.
Note: You will only need to change the external_url in gitlab.rb, no other config file should have to be edited for this.
Edit#2: As @emeraldjava stated there is an option in the configuration file for using another unicorn port: #unicorn['port'] = '8080'